Enhancing Continuous-Variable Quantum Key Distribution by State Preparation With Shannon-Kotel'nikov Maps

Abstract

We propose a continuous-variable quantum key distribution protocol that uses Shannon-Kotel'nikov maps for preparing coherent quantum states. Our protocol has similarities with the no-switching protocol in the sense that it requires that both quadratures need to be measured. It is also a Gaussian modulated protocol, because the secret key is to be extracted from Gaussian parameters. The use of this kind of map in the preparation of coherent states allows the increase in the source-to-distortion ratio (SDR) between Alice and Bob, thus making information reconciliation easier. This increase in SDR is due to the use of nonlinear maps of higher dimension instead of simply raising Alice's variance. We analyze here two kind of maps: the uniform Archimedes' spiral and the geodesics on a flat torus. We assess the security of our protocol through simulations. In order to do that, we simulate the optimal feedforward attack together with a maximum-likelihood receiver, then we use Kraskov's first algorithm to estimate the mutual information.